Stephen Boyd-《Convex Optimization》

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Convex Optimization Stephen boyd Department of Elcctrical Enginccring Stanford universitv Lieven Vandenberghe Electrical Engineering Department University of California. Los Angeles CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paolo, Delh Cambridge University Press The Edinburgh Building, Cambridge, CB2 &RU, UK Published in the United States of America by Cambridge University Press, New York http://www.cambridge.org Informationonthistitlewww.cambridge.org/9780521833783 Cambridge University Press 2004 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements no reproduction of any part may take place without the written permission of Cambridge University Press First published 2004 Seventh printing with corrections 2009 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the british library Library of Congress Cataloguing-in-Publication data boyd, Stephen p Convex Optimization/ Stephen Boyd Lieven Vandenberghe Includes bibliographical references and index ISBN0521833787 1. Mathematical optimization. 2. Convex functions. I. Vandenberghe, Lieven. II. Title QA402.5.B692004 2003063284 ISBN 978-0-521-83378-3 hardback Cambridge University Press has no responsiblity for the persistency or accuracy of URls for cxtcrnal or third-party internet websites referred to in this publication, and docs not tee that any content on is or will remain. accu Anna, Nicholas and nora Daniel and Margriet Contents Prefa 1 Introduction 1.1 Mathematical optimization 1.2 Least-squares and linear programming 4 1.3 Convex optimization 1. 4 Nonlinear optimization 1.5 Outline 1.6 Notation 14 Bibliography Theory 19 2 Convex sets 21 2.1 Affine and convex sets 21 2.2 Some important examples 27 2.3 Operations that preserve convexity 35 2.4 Generalized inequalities 2.5S 2.6 Dual cones and generalized inequalities 51 Bibliograph 59 Exercises 60 3 Convex functions 67 3.1 Basic properties and examples 67 3.2 Operations that preserve convexity 3.3 The conjugate function 90 3.4 Quasiconvex functions 95 3.5 Log-concave and log-convex functions 104 3.6 Convexity with respect to generalized inequalities .108 Bibliograph excises 113 Content: 4 Convex optimization problems 127 4.1 Opti on problems 127 4.2C 136 4.3 Linear optimization problems 146 4.4 Quadratic optimization probl 152 4.5 Geometric pr g 160 4.6 generalized inequality constraints 167 4.7 Vector optimization 174 Bibliography 188 excises 189 5 Duality 215 5.1 The Lagrange dual function ..215 5.2 The lagr dual problem 223 5. 3 Geometric interpretation 232 5.4 Saddle-point interpretation 237 5.5 optimality conditions ..241 5.6 Perturbation and sensitivity ana lysis 249 5.7 Exampl 253 5. 8 T heorems of alternatives 258 5.9 Generalized inequalities 264 Bibliograph 272 Xercises 273 I Applications 289 6 Approximation and fitting 291 6.1 Norm approximation 291 6. 2 Least-norm probler 302 6. 3 Regularized approximation 05 6. 4 Robust approximation 6.5 Function fitting and interpolation 324 Bibliography 343 E× excises 44 7 Statistical estimation 351 7.1 Parametric distribution estimation 351 7. 2 Nonparametric distribution estimation 359 7.3 Optimal detector design and hypothesis testing 364 7. 4 Chebyshev and Chernoff bounds 374 7.5 Experiment design 384 Bibliography 392 Exerci 393 Content: 8 Geometric problems 397 8.1 Projection on a set 397 8.2 Distance between sets 402 8.3 Euclidean distance and angle problems 405 8.4 Extremal volume ellipso 410 8.5 Centering 416 8.6 Classificati 422 8.7 Placement and location 432 8.8 Floor planning 438 Bibliography 446 Exercises 447 I Algorithms 455 9 Unconstrained minimization 457 9.1 Unconstrained minimization problems 45′ 9.2D 463 9.3 Gradient descent method .466 9.4 Steepest descent method 475 9.5 Newtons method 484 9.6 Self-co 9.7 Implementation lography 10 Equality constrained 521 10.1 Equality constrained minimization problems .521 10.2 Newton's method with equa lity constraints 525 10.3 Infeasible start Newton method 531 10.4 Implementation 542 Bibliograph E× excises 557 11 Interior-point methods 561 l1.1 Inequality constrained minimization problems 561 11.2 Logarithmic barrier function and central path 562 11.3 The barrier method 568 11.4 Feasibility and phase I methods 11.5 Com plexity analysis via self-concordance 585 11.6 Problems with generalized inequalities 596 11.7 Primal-dual interior-point methods 11. 8 Implementation 615 Bibliography 621 Ex xercises 623 【实例截图】
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